'The territory of Abkhazia has been completely liberated from Georgian occupiers,' the statement said. 'Measures are being taken to render harmless bandit groups hiding in forests and mountain areas.'
Georgian forces were routed on Monday in Sukhumi, the capital of Abkhazia, which has been seeking greater autonomy from the Tbilisi government since 1989.
Georgian officials in Tbilisi said their leader, Eduard Shevardnadze, had flown to the central city of Kutaisi, where he was expected to meet local security forces.
The capture of Sukhumi and the advance of Abkhazian forces further south down the coast were the culmination of an offensive launched last month which shattered a Russian-sponsored ceasefire in the region after more than 1,000 deaths in a year of fighting.
The fighting has created a mass refugee problem, with more than 100,000 people, mostly Georgians, following the soldiers on foot, by car, lorry or tractor. Georgia's Interior Ministry said a civil helicopter flying to pick up refugees in the region had crashed in bad weather on Thursday, killing about six people on board.
The defeat has sapped Georgian morale and cast the country into deep uncertainty less than two years after independence from the Soviet Union. On Thursday, the rebels swept the last Georgian forces out of Abkhazia, advancing some 90km (65 miles) in a single day as panicking government troops scattered before them.
The rout ended all attempts among the fleeing Georgians to patch up a rift between Mr Shevardnadze's forces and a rival Georgian army fielded by the ousted president, Zviad Gamsakhurdia. Gun battles broke out between the two chaotic forces as they escaped, either south-east towards Gamsakhurdia territory or north into the foothills of the Caucasus mountains.
Mr Gamsakhurdia reappeared last week in his stronghold of Zugdidi, after nearly two years in exile, while Mr Shevardnadze was defending Sukhumi. Tens of thousands of refugees have flooded into Zugdidi.
Mr Gamsakhurdia commands strong support across western Georgia, an ethnically distinct region whose people speak a separate dialect from Tbilisi's in the east.
In Kiev, the Ukrainian Foreign Ministry denounced the Abkhazian advance as a violation of the ceasefire and said Russia had failed in its role as a mediator.
Mr Shevardnadze had visited Kiev twice in recent months to ask Ukraine to act as an intermediary in the conflict.